Sure, that could potentially be the case. But as said before, I would argue that it does not seem unreasonable to me that you generally can increase BB(n) to twice BB(n) with one or a few additional states by slightly tweaking the machine. And that would be enough to get BB(n) - BB(n - 1) >= BB(n) which together with the size of BB(n) prevents really small differences. But I of course see that proving that you can increase the length of the output of any busy beaver by some constant using some number of additional states is far from trivial.
That must of course be BB(n) - BB(n - 1) >= BB(n - 1). Also I have to retract the correction from a few comments ago, the currently best lower bound for BB(6, 2) is indeed 10 ⇈ 15, I looked at an outdated source when writing the correction.